Abstract: An $(h,g)$ Sidon set is a set $S$ of integers with the property that the coefficients of $(\sum_{s \in S} z^s)^h$ are bounded by $g$. These arose naturally is Simon Sidon's study of Fourier Series, and have become a standard topic in combinatorial number theory. I will present joint work with Greg Martin giving constructions of such sets, and discuss numerous open problems.